THE NEW THEORY OF SOLUTIONS. 381 



Now, in the case of even a weak solution it is evident 

 that this volume-correction must be considerable. In the case 

 of many liquids it appears that the actual volume occupied 

 by their molecules under ordinary conditions is about one- 

 third of the total volume, consequently, on using such a 

 liquid as a solvent, the space in which the dissolved mole- 

 cules may oscillate is much smaller than the volume of the 

 solution. Why, then, should solutions conform so closely 

 to the ideal gaseous laws ? Why should values of the 

 molecular weight even in strong solutions approximate 

 to the theoretical value ? Nernst has pointed out the 

 reason by calling attention to the fact that the properties of 

 solutions have not been investigated to any extent by direct 

 measurements of osmotic pressure, but by indirect methods 

 making use of freezing-point, vapour-pressure, etc. Now 

 these methods are concerned with the separation of solvent 

 from dissolved substance (see vol. ii., p. 184), and although 

 correlated with osmotic pressure in the manner already in- 

 dicated, they do not in reality give measures of the osmotic 

 pressure but of the osmotic work, or the work required to 

 remove unit volume of solvent from the solution. Let P be 

 the gaseous pressure of a substance, and when the substance 

 is dissolved in a solvent, other things remaining the same, 

 let P be raised in the ratio of P : P/( 1 - (3), where /3 is the 

 volume-correction due to the molecules of the solvent. 

 Even although this is so the osmotic work will still be 

 P, for the change of volume which the pressure P/(i - ,3) 

 has to effect is no longer unity but 1 - /3. For this reason 

 the volume-correction does not affect the results of freezing- 

 point, vapour-pressure, and other methods based on the 

 same principle. These results are only affected by the 

 attractive forces included in the o-term of the equation, and 

 since the osmotic pressure will be larger or smaller than the 

 theoretical value according as a is positive or negative, it 

 follows that the molecular weight will increase or diminish 

 with the concentration according as the attraction of the 

 molecules of the dissolved substance for each other is greater 

 or less than the attraction of the molecules of the dissolved 

 substance for those of the solvent. 



